It looks like Arizona Gov. Jan Brewer’s endorsement wasn’t as important for candidates in Tuesday’s Republican primary as their own name recognition.

Ms. Brewer surprised political onlookers by endorsing 21 state candidates in the GOP primary, choosing for the most part moderate Republicans who supported her controversial 2013 move to expand Medicaid under the federal Affordable Care Act, or Obamacare.

The lame-duck Republican governor picked some winners, starting with Michele Reagan, who won the nod for Secretary of State in a tight three-way primary.

In the showcase race for governor, however, Ms. Brewer whiffed. Her candidate, former Mesa Mayor Scott Smith, finished second to state Treasurer Doug Ducey in the six-way race for the Republican gubernatorial nomination.

In the legislative races, Ms. Brewer appeared to break even, but analysts pointed out that there was a more powerful factor at play: incumbency. Candidates who now serve or have recently served in the state legislature were much more likely to win the party’s nod than newcomers, whether they had the governor’s endorsement or not.

“If there’s a pattern here, it’s an incumbency pattern,” said Arizona political analyst Mike O’Neil. “When she endorsed an incumbent, they won. When she endorsed a non-incumbent against an incumbent, she lost.”

For example, Ms. Brewer threw her support behind businessman Jeff Schwartz against state Rep. John Kavanagh in the Senate District 23 race, but Mr. Kavanagh, a conservative favorite, won with 53 percent of the vote, according to figures posted by the Arizona Secretary of State.

On the other hand, Brewer-backed state Sen. Bob Worsley won his primary re-election bid by 53 percent to 46 percent against Ralph Heap, the more conservative candidate backed by the grass-roots Alliance for Principled Conservatives.

The alliance had endorsed a slate of candidates almost entirely at odds with Ms. Brewer’s picks. Possibly the only candidate they agreed on was Mark Brnovich, who defeated embattled incumbent Tom Horne in the attorney general primary.

Alliance chair Christine Bauserman said she was pleased with the outcome of the primary, saying, “We actually gained ground.”

While Mr. Smith fell short in the gubernatorial contest, Mr. O’Neil said he wouldn’t have come as close without the governor’s endorsement. Mr. Ducey won with 37 percent of the vote, followed by Mr. Smith with 22 percent.